Algorithms and Uncertainty Sets for Data-Driven Robust Shortest Path Problems

TL;DR

This paper explores data-driven robust shortest path algorithms using real traffic data, comparing various uncertainty sets and introducing a new efficient algorithm for ellipsoidal sets that outperforms existing solvers.

Contribution

It constructs and evaluates multiple uncertainty sets from real-world data, and develops a novel, more efficient algorithm for ellipsoidal uncertainty sets in robust shortest path problems.

Findings

Ellipsoidal uncertainty sets perform well in practice.

The new algorithm significantly outperforms state-of-the-art solvers.

Data-driven approaches improve robustness in shortest path planning.

Abstract

We consider robust shortest path problems, where the aim is to find a path that optimizes the worst-case performance over an uncertainty set containing all relevant scenarios for arc costs. The usual approach for such problems is to assume this uncertainty set given by an expert who can advise on the shape and size of the set. Following the idea of data-driven robust optimization, we instead construct a range of uncertainty sets from the current literature based on real-world traffic measurements provided by the City of Chicago. We then compare the performance of the resulting robust paths within and outside the sample, which allows us to draw conclusions what the most suited uncertainty set is. Based on our experiments, we then focus on ellipsoidal uncertainty sets, and develop a new solution algorithm that significantly outperforms a state-of-the-art solver.